# Thread: geometry in complex numbers

1. ## geometry in complex numbers

Represent the following region in the complex plane by equations or inequalities in the variable
z.

All the points outside a circle of radius 3, centered at x=-1, y=-2.

i drew the circle -4< x < 2 and -5<y<1

so how do we do the equation or the inequality?

2. Originally Posted by sandy
Represent the following region in the complex plane by equations or inequalities in the variable
z.

All the points outside a circle of radius 3, centered at x=-1, y=-2.

i drew the circle -4< x < 2 and -5<y<1

so how do we do the equation or the inequality?
A circle of radius $\displaystyle R$ around a complex number $\displaystyle z_0\in\mathbb{C}$ is defined to be $\displaystyle \left\{z\in\mathbb{C}:|z-z_0|=R\right\}$

3. Originally Posted by Drexel28
A circle of radius $\displaystyle R$ around a complex number $\displaystyle z_0\in\mathbb{C}$ is defined to be $\displaystyle \left\{z\in\mathbb{C}:|z-z_0|=R\right\}$
i didnt understand, the equation of a circle is |z-z_0|=R but how do we do the above as an inequality or equation?

4. $\displaystyle \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}$.

5. Originally Posted by Plato
$\displaystyle \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}$.
oh ok thankyou very much now i understood what they want and how to solve questions like that. thanks again